Partial Factorization

Algebra Level 2

If 3 x + 5 2 x 2 − 5 x − 3 = A x − 3 − B 2 x + 1 \dfrac{3x+5}{2x^2-5x-3} = \dfrac{A}{x-3} - \dfrac{B}{2x+1} is an algebraic identity for constants A A and B B , then find A + B A + B .


The answer is 3.

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Jessey Uche-Nwichi by Jessey Uche-Nwichi , 17, Nigeria

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1 solution

Naren Bhandari
Feb 23, 2017

3 x + 5 = ( 2 A − B ) x + ( A + 3 B ) 3x +5 = (2A -B)x + (A +3B) Here 2 A − B = 3 ⋯ ( 1 ) 2A -B = 3\cdots(1)

A + 3 B = 5 ⋯ ( 2 ) A+3B = 5\cdots(2)

Solving equation(1) and (2)

A = 2 A = 2 and B = 1 B = 1

  • Therefore, A + B = 3 A+B = \boxed{3}
1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Naren Bhandari - Great Solution

Moulik Bhattacharya - 4 years, 3 months ago

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